Answer:

Step-by-step explanation:
Assuming that the equation is
with initial condition
. We have,
, hence we can say that
and
in the general form of the first order linear differential equation:

The integrating factor is given by:
. Thus, multiplying the entire equation by the integrating factor:
. This means that:
![\frac{d[e^{3x}y]}{dx} = 24e^{3x}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5Be%5E%7B3x%7Dy%5D%7D%7Bdx%7D%20%3D%2024e%5E%7B3x%7D)
then
. Applying the initial condition:
and therefore, 
Assuming that the equation is
with initial condition
. We have,
, hence we can say that
and
in the general form of the first order linear differential equation:

The integrating factor is given by:
. Thus, multiplying the entire equation by the integrating factor:
. This means that:
![\frac{d[e^{\frac{x}{3}}y]}{dx} = 8e^{\frac{x}{3}}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5Be%5E%7B%5Cfrac%7Bx%7D%7B3%7D%7Dy%5D%7D%7Bdx%7D%20%3D%208e%5E%7B%5Cfrac%7Bx%7D%7B3%7D%7D)
then
. Applying the initial condition:
and therefore, 